How to blur a single layer in a grease pencil object?
I don't think you can but you can approach it by using a combination of modifiers, which support layers.
Let's say you have two strokes created with the same material but on two different layers :

Add a Thickness modifier, in the influence set it to your target layer

Add an Opacity modifier, set the layer. Set the mode to Hardness and decrease it.

Add another Opacity modifier, set the layer again. Decrease the strength or the factor.

You might want to disable or enable Self Overlap on the material if you want to decrease the artifacts.

The artifacts are particularly prominent on sharp turns.